Question $3(15$ pts$).$ During the production of $Fe$ from iron oxide $(F{e}_2{O}_3)$ the main reaction is the following:

$F{e}_2{O}_3+3C2Fe+3CO$

However, during the main reaction the following undesired side reaction also occurs:

$F{e}_2{O}_3+C2$FeO$+CO$

In the process $600lbm$ of carbon $($C$)$ is mixed with $1$ ton of iron oxide and the output of the process includes $1200lbm$ of $Fe,183lbm$ of FeO and $85lbm$ of $F{e}_2{O}_3.$ Calculate the following for this process:

a$)$ The percentage excess of $C$ based on the main reaction.

b$)$ The percentage conversion of iron oxide to $Fe.$

c$)$ The amount of carbon usage and the amount of $CO$ produced $($in $lbm)$ per ton of iron oxide feed.

d$)$ The selectivity of $Fe$ over FeO.